Analysis of Weakly Symmetric Mixed Finite Elements for Elasticity

TL;DR

This paper analyzes weakly symmetric mixed finite element methods for linear elasticity, providing error estimates and numerical verification, especially effective in the incompressible limit.

Contribution

It offers a comprehensive error analysis for known weakly symmetric mixed finite element methods, including a posteriori estimates valid in both compressible and incompressible cases.

Findings

Error estimates are established for the methods.

A posteriori estimates are derived for different cases.

Numerical examples confirm theoretical results.

Abstract

We consider mixed finite element methods for linear elasticity where the symmetry of the stress tensor is weakly enforced. Both an a priori and a posteriori error analysis are given for several known families of methods that are uniformly valid in the incompressible limit. A posteriori estimates are derived for both the compressible and incompressible cases. The results are verified by numerical examples.